The Derivation of Electric field due to a dipole at any point is not clear to me. Can anyone help me out understand it better???

Electrostatics question based on earthing of spherical shell

an object has a charge of 2c and gains 10^19 electrons. the net chaarge on the object becomes??

A wire with a linear charge density lambda forms a quarter of a cjrclenof radius R and is placed asa shown in thefigure with its centre of curvature at the origin O the electric field at O will be

Find the value of q so that system remains in equilibrium.. figure attached below

Need to find the time taken for the dipole to come back to eqm